Multi-source-extractors are functions that extract uniform randomness from multiple (weak) sources of randomness. Quantum multi-source-extractors were considered by Kasher and Kempe (for the quantum-independent-adversary and the quantum-bounded-storage-adversary), Chung, Li and Wu (for the general-entangled-adversary) and Arnon-Friedman, Portmann and Scholz (for the quantum-Markov-adversary). One of the main objectives of this work is to unify all the existing quantum multi-source adversary models. We propose two new models of adversaries: 1) the quantum-measurement-adversary (qm-adv), which generates side-information using entanglement and on post-measurement and 2) the quantum-communication-adversary (qc-adv), which generates side-information using entanglement and communication between multiple sources. We show that, 1. qm-adv is the strongest adversary among all the known adversaries, in the sense that the side-information of all other adversaries can be generated by qm-adv. 2. The (generalized) inner-product function (in fact a general class of two-wise independent functions) continues to work as a good extractor against qm-adv with matching parameters as that of Chor and Goldreich. 3. A non-malleable-extractor proposed by Li (against classical-adversaries) continues to be secure against quantum side-information. This result implies a non-malleable-extractor result of Aggarwal, Chung, Lin and Vidick with uniform seed. We strengthen their result via a completely different proof to make the non-malleable-extractor of Li secure against quantum side-information even when the seed is not uniform. 4. A modification (working with weak sources instead of uniform sources) of the Dodis and Wichs protocol for privacy-amplification is secure against active quantum adversaries. This strengthens on a recent result due to Aggarwal, Chung, Lin and Vidick which uses uniform sources.

翻译：多重源提取器是一种从多个（弱）随机源中提取均匀随机性的函数。Kasher与Kempe（针对量子独立敌手模型和量子有界存储敌手模型）、Chung、Li与Wu（针对一般纠缠敌手模型）以及Arnon-Friedman、Portmann与Scholz（针对量子马尔可夫敌手模型）曾研究过量子多重源提取器。本研究的主要目标之一是统一现有所有量子多重源敌手模型。我们提出两种新型敌手模型：1）量子测量敌手模型（qm-adv），该模型利用纠缠态与后测量过程生成侧信息；2）量子通信敌手模型（qc-adv），该模型通过多源间的纠缠与通信生成侧信息。研究结果表明：1. qm-adv是已知所有敌手模型中最强的，即其他所有敌手的侧信息均可由qm-adv生成。2.（广义）内积函数（实际上是一类广义两两独立函数）仍可作为有效的提取器对抗qm-adv，其参数与Chor和Goldreich方案相匹配。3. Li提出的（抗经典敌手的）非弹性提取器在量子侧信息环境下仍保持安全性。该结果蕴含了Aggarwal、Chung、Lin与Vidick关于均匀种子非弹性提取器的结论。我们通过完全不同的证明方法增强其结论，使得Li的非弹性提取器在种子非均匀时仍能抵抗量子侧信息攻击。4. 对Dodis与Wichs隐私放大协议的修正方案（使用弱随机源替代均匀随机源）可抵御主动量子敌手攻击。这增强了Aggarwal、Chung、Lin与Vidick近期使用均匀随机源的研究成果。